The present invention relates to a computerized method for three-dimensional fluid simulation to analyze fluid flows around an object.
Heretofore, various fluid simulations in which the state of fluid (velocity, pressure, etc.) flowing around an object are analyzed by the use of a computer were proposed and utilized to develop the geometry of an object, for example, an arrangement of dimples of a golf ball in order to decrease the air resistance (drag) and improve the flight performance.
As well known, in a computerized fluid simulation, a flow domain or a three-dimensional space in which the fluid flows is split into subdomains (often called elements or cells) to generate a grid or mesh. In a domain near the object, the fluid flow is expected to become complex. But in a domain relatively away from the object, the fluid flow is expected to be simple. Therefore, in a grid generation, it is desirable that the domain far from the object is split into a coarse grid or mesh (namely, the grating density is lower) from the aspect of the computational efficiency although the domain near the object has to be split into a fine grid or mesh (namely, the grating density is higher) in order to increase the spacial resolution and thereby to enable detailed analyses of the fluid flow.
In order to achieve such variable spacial resolution, if the flow domain or the above-mentioned 3-D space is non-uniformly split with respect to each of three degrees of freedom (triaxial) of three dimensions, then direct methods such as FFT plus block cyclic reduction method can not be used in the computation, and it becomes necessary to use iteration methods such as Algebraic Multigrid Method (AMG method) and Full Multigrid Method (FMG method). As a result, there is a problem such that the computational time is significantly increased.
On the other hand, if the flow domain is uniformly split with respect to each of three degrees of freedom of three dimensions, into a uniform structured grid, then it is necessitated that the number of the subdomains (cells) becomes enormous in order to achieve sufficient analytical accuracy. In this case too, there is a problem such that the computational time is unfavorably increased.